Late last month, a ragtag group of several hundred liberal activists ventured to the centre of America's economic universe – Wall Street – to protest against what they saw as the country's growing income inequality and the stranglehold of corporate money over US democracy. The Occupy Wall Street (OWS) movement hoped to attract thousands of protesters, but the turnout ended up being disappointingly smaller. Coverage of the protests was largely restricted to liberal media outlets and a snarky piece in the New York Times captured the sentiments of many when it dismissed them as "carnival" and "street theatre". One could be forgiven for dismissing the demonstrations as simply another failure of progressive populist politics in an era where populist energy is generally restricted to the anti-government, conservative right.

What a difference a month makes. Not only has OWS survived, it has captured the imagination of multitudes of embittered Americans. It has become a national force with the very real potential to roil American politics fundamentally. Other groups have sprung up in cities across the US and are now branching out internationally, including London.

American unions are jumping on the bandwagon, showing solidarity with a movement that shares many of labour's anti-corporate views. So, too, are Democratic politicians who detect a shift in the political winds. Mainstream media now treat the "Occupiers" as legitimate political protesters rather than a collection of clueless hippies. In a poll by Time, 54% of respondents rated the Wall Street protests positively, with 25% saying they had a "very favourable" opinion of them.

So what exactly is happening here? In a nutshell, Americans are ticked off. Millions are struggling financially; many are out of a job or are underemployed. They can't pay their bills. They are falling deeper into personal debt. They are losing hope that things will improve in the foreseeable future. Worst of all, while they are falling further behind a small minority appears to be leaping further ahead.

Wall Street and the big banks caused the market crash that cost millions of jobs and plunged the US economy into near-depression. Yet three years later, the country's financial elite continues to prosper while the other 99% suffers. Meanwhile, Washington, due mainly to the unceasing obstructionism of the Republican party, seems completely incapable of arresting America's decline.

In some ways, what's most amazing about OWS – and the support it's receiving – is not that it happened, but frankly why the hell it took so long.

Throughout American history, populist movements have arisen in similar situations. In the early 20th century, progressivism arose, in part, as a response to robber-baron capitalism run amok. In the early 1930s, after the worst economic downturn in American history, populist demagogues such as Huey Long captured the sentiments of millions. Indeed, the infamous proclamation by Franklin Roosevelt in 1936 that he welcomed the hatred of the plutocratic class was a reflection of the political vulnerability that he felt not from the right but, rather, a radicalised left. It's a problem Barack Obama would love to have.

And this is one of the conundrums of recent American politics. In the wake of a disastrous war prosecuted by a Republican president and an economic crisis sparked by Wall Street greed, the response was not from the left but from a rightwing populist movement that aimed its hatred squarely at "big government" and the supposed socialist in the White House.

Such anti-government sentiment – and the inclination to view government as the root of America's problems – is at pace with the conservative populist sentiments that have defined US politics since the late 1960s. It's been a long time since economic, anti-corporate and liberal populism has lit a fire among ordinary Americans. As for popular protest, it's been even less successful in mobilising public opinion.

From this perspective, OWS has arisen not because of the left's activism, but despite it. Focusing on electoral victories and legislative accomplishments, the left has failed to push an effective populist movement, focusing its energy more on social issues than economic ones. Democratic leaders have stayed at arm's length from the party's activist base for fear of being stained by their perceived political excesses (a position that has rightly alienated a generation of liberals). Considering these larger failures of the left, it seems almost appropriate that OWS has come about in such an organic and ad hoc manner.

It raises the question of what this all means for American politics and, in particular, next year's presidential election. There is certainly the possibility that the demonstrators, many of whom are firmly ensconced on the fringes of American politics, will spark a backlash or that the movement, which still lacks a clear agenda, will fizzle out.

But there is another real possibility – that OWS will affect the near-term trajectory of American politics. While many of the protesters are unhappy with the current progressive president, their grievances and demands are very much at one with Obama's emerging re-election strategy.

The Occupiers have called themselves the other 99% – to contrast themselves from the richest 1%. For a president intent on running as an economic populist, a populist political movement might just be what the doctor ordered. No doubt Obama would have liked to see a movement like this a few years ago; it might have helped him pass his agenda through a recalcitrant Congress, but, hey, better late than never (and on this, he is hardly blameless).

Not surprisingly, the Republican response to the protests has been one of dismissal, even contempt. House majority leader Eric Cantor called the Occupiers "mobs". Republican frontrunner Mitt Romney has accused them of "class warfare" (a charge clearly meant as an insult though it's one the protesters would gladly embrace). Presidential contender Herman Cain went further and called them "anti-American".

But Republicans may be underestimating the power of the Occupiers' message. Elizabeth Warren, a darling of the left and a Democratic Senate candidate in Massachusetts, was recently spoofed in an ad said to have been pushed on YouTube by the state's Republican party, though it has denied responsibility. She is portrayed as a vindictive and profane partisan. The "fake Warren" suggests that if elected she would propose legislation that would allow every American to go to Wall Street and put their foot in a particularly sensitive area of the male anatomy. This is seen by Massachusetts Republicans as a liability for Warren.

But perhaps the opposite is true. If one surveyed the American people I'd imagine a good number of them would relish the opportunity to kick Wall Street in the groin. If OWS continues, they might just get their metaphorical wish.

• This article was amended on 19 October 2011 to make it clear that the Massachusetts State GOP has denied responsibility for putting out an advertisement spoofing Democratic senate candidate Elizabeth Warren.